Method and device for controlling power generators of a subgrid within an interconnected grid

ABSTRACT

Disclosed is a subnetwork controller (TNR) for a subnetwork (TN) within an interconnected grid (NV), which controller controls power generators (G), subnetworks or loads (L) of the subnetwork in accordance with sensor-captured internal measured variables (y i ) and sensor-captured external measured variables as well as external controlled variables (v i ) of the subnetwork (TN) in such a way that a dynamic behaviour of the subnetwork (TN) in relation to its adjacent subnetworks corresponds to a defined desired behaviour.

The invention relates to a method and to a device, in particular a sub-grid controller, for controlling power generators of a sub-grid within an interconnected grid.

Electrical grids, for instance the European electrical grid, can consist of a multiplicity of sub-grids. For instance the German electrical grid is a sub-grid within the European electrical grid. This sub-grid can itself consist of various sub-grids. For instance, the German electrical grid comprises a sub-grid for supplying the urban area of the city of Hamburg and a sub-grid for supplying the Munich urban area. Each sub-grid consists of a plurality of nodes or power supply buses, which are connected to one another via lines. Power generators and consumers or loads can be connected to the nodes. It is also possible, however, for subnetworks, which are hierarchically lower-level sub-grids of the sub-grid, to be connected to the nodes. Each sub-grid can in itself already have a relatively high complexity. The loads may be aggregated loads, for example the power supply load of a housing estate or factory. The power generators, for example, are gas turbines or coal-fired power stations. The subnetworks can in turn consist of a plurality of nodes connected to one another via lines, to which nodes are attached power generators, loads or sub-subnetworks. The various distribution grids are usually connected to one another via high-voltage transmission grids.

Distributed renewable and, in some cases, also controllable electricity generators or power generators are being used increasingly in electrical grids. A possible result of this, for instance, is that in a country such as Germany, the maximum possible amount of power generated by renewable energy sources reaches or even exceeds the magnitude of the total load of the country. For instance, depending on weather conditions, the power generated by the renewable energy sources can surpass at least temporarily, for instance for hours or weeks, the total consumption of power in the country concerned, in particular given future expansion of the electrical grids by deployment of further renewable energy sources.

With conventional electrical grids such as those currently in use, however, there is a problem with the further expansion of the electrical grid by renewable energy sources in that a certain proportion of conventional power generators, in particular coal-fired power stations or nuclear power stations, are needed in order to achieve grid stability. The grid stability is analyzed, for example, on the basis of dynamically non-linear simulations of the transmission grid. These non-linear simulations are based on detailed models of a relatively small number of conventional power generators. The loads contained in the electrical grid are typically represented by distribution-grid areas containing connected or aggregated loads and a few non-controlled distributed generators. The grid stability is achieved by operating the conventional power generators according to suitable active-power and reactive-power rules. The larger the number of different distributed, in particular renewable, power generators, within the grid, the less possible it becomes to achieve or ensure stability of the entire interconnected grid using the conventional techniques, in particular simulation techniques.

Hence an object of the present invention is to provide a method and a device for controlling components such as power generators, loads and subnetworks of a sub-grid within an interconnected grid, which method and device can be used to achieve a grid stability even for a relatively large number of distributed power generators.

This object is achieved according to the invention by a sub-grid controller having the features stated in claim 1.

According to said claim, the invention provides a sub-grid controller for a sub-grid within an interconnected grid, which controller controls power generators, loads or subnetworks of the sub-grid according to sensor-detected internal measured variables and/or sensor-detected external measured variables and external manipulated variables of the sub-grid in such a way that a dynamic behavior of the sub-grid with respect to its neighboring sub-grids corresponds to a defined target behavior. The external manipulated variables can be defined by a hierarchically higher-level controller, in particular by a controller of the interconnected grid.

A fundamental idea of the invention is to break down or subdivide a large, highly complex electrical grid into different areas or sub-grids, wherein each of these areas can be reduced to smaller or less comprehensive dynamic models for the area concerned. The discrete area may be, for example, the area of a distribution grid, in particular a local distribution grid. In addition, a group of a few large conventional generators in the area of a transmission grid can form a discrete area of this type.

In a possible embodiment of the sub-grid controller according to the invention, the sub-grid controller calculates a control vector {right arrow over (u)} for the power generators, loads and subnetworks from a vector {right arrow over (y)} of the internal measured variables and a vector {right arrow over (v)} of the external measured variables and manipulated variables as follows:

{right arrow over (u)}=K·y+L·{right arrow over (v)}, where

K is an output feedback matrix, and

L is a feedforward matrix.

This embodiment has the advantage that calculating the control vector has a relatively low computational complexity and the calculation can be performed relatively quickly.

In another possible embodiment of the sub-grid controller according to the invention, the external measured variables of the sub-grid are detected by sensors, which are arranged on connecting lines between the sub-grid and its neighboring sub-grids.

This embodiment has the advantage that the external measured variables can be detected accurately by sensors, and the control vector calculated therefrom allows precise, reliable control of the power generators.

In another possible embodiment of the sub-grid controller according to the invention, the internal measured variables are detected by sensors, which are arranged on lines and devices within the sub-grid.

This embodiment also has the advantage that the measured variables, i.e. the internal measured variables, can be detected accurately by sensors, and the control-vector control variables calculated therefrom allow precise open-loop and closed-loop control of the power generators.

In another possible embodiment of the sub-grid controller according to the invention, the sub-grid controller receives from an operator of the interconnected grid the target behavior and the external setpoint values. The received target behavior is in this case intended to stabilize the interconnected grid.

This has the advantage that the operator of the interconnected grid can define a desired target behavior for the various sub-grids so that the interconnected grid composed of the sub-grids behaves as stably as possible in accordance with the requirements from the interconnected-grid operator.

In another possible embodiment of the sub-grid controller according to the invention, the instantaneous state of the sub-grid can be calculated by the following differential equation:

{dot over ({right arrow over (x)})}=A·{right arrow over (x)}+B ₁ ·{right arrow over (u)}+B ₂ ·{right arrow over (v)}+B ₃ ·{right arrow over (w)}

where

-   {right arrow over (x)} is the state vector of the sub-grid, -   {right arrow over (u)} is the control vector for controlling the     controllable power generators, loads and subnetworks within the     sub-grid, -   {right arrow over (v)} is the vector of the sensor-detected external     measured variables and external manipulated variables, and -   {right arrow over (w)} is the disturbance vector,     and where

A, B₁, B₂, B₃ are matrices.

This embodiment has the advantage that the internal state of the sub-grid can be calculated precisely for each point in time and it is thereby possible to respond quickly to instabilities within the sub-grid.

In another possible embodiment of the sub-grid controller according to the invention, the vector {right arrow over (y)} of the internal measured variables of the sub-grid can be calculated by the following equation:

{right arrow over (y)}=C·{right arrow over (x)}+D ₁ ·{right arrow over (u)}+D ₂ ·{right arrow over (v)}+D ₃ ·{right arrow over (w)}

where

-   {right arrow over (x)} is the state vector of the sub-grid, -   {right arrow over (u)} is the control vector for controlling the     controllable power generators, loads and subnetworks within the     sub-grid, -   {right arrow over (v)} is the vector of the sensor-detected external     measured variables and external manipulated variables, and -   {right arrow over (w)} is the disturbance vector,     and where

C, D₁, D₂, D₃ are matrices.

This embodiment has the advantage that the vector of the internal measured variables can be calculated quickly and reliably so that the open-loop and/or closed-loop control of the components of the sub-grid can be performed precisely and promptly.

In another possible embodiment of the sub-grid controller according to the invention, an output vector {right arrow over (z)} of the output variables of the sub-grid can be calculated by the following equation:

{right arrow over (z)}=E·{right arrow over (x)}+F ₁ ·{right arrow over (u)}+F ₂ ·{right arrow over (v)}+F ₃ ·{right arrow over (w)}

where

-   {right arrow over (x)} is the state vector of the sub-grid, -   {right arrow over (u)} is the control vector for controlling the     controllable components of the sub-grid, -   {right arrow over (v)} is the vector of the sensor-detected external     measured variables and external manipulated variables, and -   {right arrow over (w)} is the disturbance vector,     and where

E, F₁, F₂, F₃ are matrices.

This embodiment has the advantage that the output variables of the sub-grid, which are relevant to the operation of the interconnected grid, can be calculated quickly and reliably.

In another possible embodiment of the sub-grid controller according to the invention, the sub-grid controller is a central controller provided in the sub-grid concerned. It is also possible here for local controllers to be implemented in the components of the sub-grid.

This embodiment has the advantage that only one central controller needs to be provided for each sub-grid and therefore the additional technical expenditure is kept under tight control.

In another possible embodiment of the sub-grid controller according to the invention, the sub-grid controller is a controller that is implemented in the sub-grid in a distributed manner.

This embodiment has the advantage that the locally implemented, distributed controllers can be located close to the power generators, loads or subnetworks and can thereby respond particularly quickly to changes that are critical to the stability of the sub-grid.

In another possible embodiment of the sub-grid controller according to the invention, the sub-grid controller controls power generators, loads and subnetworks within a power distribution grid and/or configures the local controllers of said components. For subnetworks, these local controllers may in particular also be hierarchically lower-level sub-grid controllers of the subnetwork.

By controlling the components of the sub-grid directly, it is possible to respond particularly quickly and reliably to changes that are critical to the stability of the sub-grid concerned or critical to the subsequent behavior with respect to the defined target behavior.

According to another aspect, the invention provides an interconnected grid, which consists of a multiplicity of sub-grids, each of which contains a sub-grid controller according to the first aspect of the invention. The interconnected grid can itself be a hierarchically lower-level sub-grid of an even larger interconnected grid. For instance, Germany can be the interconnected grid of a plurality of sub-grids within Germany. In addition, Germany can be a sub-grid of the European interconnected system, an even larger interconnected grid.

According to another aspect of the invention, the invention provides a method for controlling components of a sub-grid within an interconnected grid having the features stated in claim 13.

According to said claim, the invention provides a method for controlling components of a sub-grid within an interconnected grid, comprising the steps:

using sensors to detect internal and external measured variables of the sub-grid;

controlling components of the sub-grid according to the sensor-detected measured variables in such a way that a dynamic behavior of the sub-grid with respect to its neighboring sub-grids corresponds to a defined target behavior.

The components may be controllable or configurable components.

Controllable components are power generators, loads or subnetworks that can be controlled in real-time and are controlled via data lines and/or control lines directly by a sub-grid controller of the sub-grid concerned. In particular, controllable subnetworks can have their own dedicated subnetwork controller that can be controlled directly by the sub-grid controller.

Configurable components such as power generators, loads or subnetworks have local controllers and are controlled locally by same. Said components can respond to local measured variables such as voltage frequency and voltage amplitude, for example by changing the active-power and reactive-power feed-in. In particular, configurable subnetworks can have their own subnetwork controller, which is configured by the sub-grid controller, e.g. by specifying a target behavior of the subnetwork, which the subnetwork controller does its best to follow.

According to a possible embodiment of the method according to the invention, the target behavior of the sub-grid is defined or set by an operator of the interconnected grid.

According to another aspect of the invention, a sub-grid controller is provided with a microprocessor which executes a control program containing program commands for implementing the method for controlling components of a sub-grid within an interconnected grid, which method comprises the steps:

using sensors to detect internal and external measured variables of the sub-grid;

controlling components of the sub-grid according to the sensor-detected measured variables in such a way that a dynamic behavior of the sub-grid with respect to its neighboring sub-grids corresponds to a defined target behavior.

A particular advantage here is that the sub-grid controller can execute a configurable control program so that it is flexible to changes in the grid topology, to the replacement of grid components or to a change in the target behavior. In addition, the control program can be transmitted via a network interface to the sub-grid controller so that it is possible to reconfigure or reprogram the sub-grid controller from a remote server, for example from a server of the interconnected-grid operator or of the operator of the sub-grid concerned.

Preferred embodiments of the method according to the invention and of the device according to the invention for controlling components of a sub-grid within an interconnected grid are explained in greater detail below with reference to the accompanying figures, in which:

FIG. 1 is a schematic diagram of an interconnected grid having a plurality of sub-grids as an example for explaining the manner of operation of the method according to the invention and the device according to the invention for controlling power generators of a sub-grid within the interconnected grid;

FIG. 2 is a schematic diagram for illustrating the manner of operation of the device according to the invention and the method according to the invention for controlling components of a sub-grid within an interconnected grid.

As FIG. 1 shows, an interconnected grid NV can consist of a multiplicity of sub-grids TN_(A), TN_(B), TN_(C) and TN_(D), which are connected to one another via connecting lines VL. Each sub-grid TN can itself consist of subnetworks or lower-level sub-grids, i.e. the interconnected grid NV can have a hierarchical structure. The interconnected grid or electrical grid can be divided into individual areas, which can each be reduced or collapsed down to smaller dynamic sub-models. For instance a distribution-grid area, which is connected to a transmission grid via a transformer, may form such an area or sub-grid TN. In particular if the separated area or the sub-grid contains a large number of distributed renewable power generators or electricity generators and/or loads having control interfaces, the operator of the sub-grid, for example the subsystem operator (DSO: Distribution System Operator) can apply special procedures in order to control the dynamic behavior such that it corresponds to a defined target behavior. The interconnected grid NV can have a hierarchical structure. For example, a plurality of low-voltage grids LV are connected to a medium-high voltage grid MV. A plurality of medium-high voltage grids MV are connected to a high-voltage grid HV. A plurality of high-voltage grids HV are connected, for example, to a European interconnected grid or network NV. Hence in the upper hierarchical levels, the sub-grids can themselves consist of sub-grids, or what are known as subnetworks.

Thus the method according to the invention takes a two-stage approach. First, the operator ISO (Transmission System Operator) of the interconnected grid or transmission grid formulates a desired dynamic behavior or target behavior for each connected area or each sub-grid TN such that the overall system stability and performance of the interconnected grid NV is maintained. This can be achieved using simulations or by a suitable controller design. In a further step or stage, the operators DSO of the individual areas or sub-grids can design a control architecture for their particular area such that the sub-grid TN concerned runs internally in a stable manner and behaves with respect to the transmission network or the interconnected grid NV dynamically in the manner specified or defined by the operator TSO of the interconnected grid by means of the target behavior for the relevant area.

In a further step, the network stability can be analyzed in terms of one or more network parameters on the basis of non-linear simulations and the reduced dynamic models contained in the previous step. The specification of the target behavior of the various areas and the implementation of this target behavior in the various areas can be performed iteratively by the sub-grid controllers TNR according to the invention until the desired dynamic behavior of each sub-grid or subarea TN corresponds to a desired target behavior with sufficient accuracy. The sub-grids or controllable subareas TN provide a stability service for the entire network or interconnected grid NV. The operators DSO of the sub-grids can receive financial compensation or remuneration, for example, from the operator TSO of the interconnected grid NV for providing this service. The operator TSO of the interconnected grid has the facility to implement one or more actuators for implementing the grid stability services. In addition, the interconnected-grid operator TSO even has the facility to shut down all the conventional electricity generators or power generators entirely if the renewable power generators are supplying the required services.

An interconnected grid NV according to the invention consists of a multiplicity of sub-grids TN, which are connected to one another via connecting lines VL. Each sub-grid TN can itself hierarchically consist of further subnetworks or sub-grids. In one possible embodiment of the interconnected grid, each sub-grid TN has a dedicated sub-grid controller TNR. In another possible embodiment it is also possible that the majority of the sub-grids TN each contain a dedicated sub-grid controller TNR according to the invention. In one possible implementation, each sub-grid controller TNR comprises a microprocessor, which executes a suitable control program for controlling power generators or controllable loads of the sub-grid TN concerned. In this case, the control program contains program commands for controlling components of the sub-grid TN. First, internal and external measured variables of the sub-grid TN are detected by sensors, and external manipulated variables of said sub-grid are captured. The external manipulated variables can be transmitted, for example, in real-time by the operator of the interconnected grid. Then the components of the sub-grid TN are controlled by the sensor-detected measured variables and manipulated variables such that a dynamic behavior of the sub-grid TN concerned with respect to its neighboring sub-grids TN corresponds to a defined target behavior, which is transmitted, for instance, by the operator TSO of the interconnected grid NV via an interface to the sub-grid controller TNR concerned.

Controllable power generators, loads and subnetworks can be controlled online by the sub-grid controller TNR of the sub-grid concerned. Configurable power generators, loads and subnetworks can be configured and then controlled locally.

FIG. 1 shows by way of example the structure of an interconnected grid comprising a plurality of sub-grids TN_(A), TN_(B), TN_(C) and TN_(D), which are connected to one another via connecting lines VL. In the example shown, a sub-grid TN_(A) is connected via two connecting lines VL1, VL2 to neighboring sub-grids TN_(B), TN_(C). Each sub-grid TN, of the interconnected grid contains a multiplicity of different loads L and generators G. The generators G are power generators, for example electricity generators, which generate power from renewable energy sources such as the sun or wind, for example. The various loads L include, for example, individual loads or consumer devices such as refrigerators or the like, or aggregated loads such as the consumers of a residential neighborhood within a local grid for instance. Measurement units such as, for instance, phasor measurement units PMU within the sub-grid TN can use sensors to detect internal measured variables y_(i) and to supply same to the sub-grid controller TNR within the sub-grid TN concerned, as shown in FIG. 1. In addition to the sensor-detected internal measured variables y_(i) the sub-grid controller TNR of the sub-grid TN also receives sensor-detected external measured variables v_(i) of the sub-grid TN. The external measured variables of the sub-grid TN are detected by sensors which are arranged on the connecting lines VL_(i) between the sub-grid TN and its neighboring sub-grids TN. In the example shown, the external measured variables V1, V2 may be a local voltage U1 and U2 and a local mains frequency f1 and f2, for instance. In this example, an input measured variable v is formed by a pair of measured variables (u_(i), f_(i)) for instance. The sub-grid controller TNR thus receives as input variables the sensor-detected internal measured variables y_(i) produced by sensors within the sub-grid TN of said controller, and sensor-detected measured variables supplied by sensors that are installed on the connecting lines VL to neighboring sub-grids TN. In addition, the TNR can receive external manipulated variables, for instance from the operator of the interconnected grid. The sub-grid controller TNR calculates from a vector y of the internal measured variables and from a vector v of the external measured variables and external manipulated variables, a control vector {right arrow over (u)} for the power generators G, subnetworks or even any controllable loads or consumers. In one possible embodiment, the control vector u for the power generators G and subnetworks and/or controllable loads is calculated from the vector y of the internal measured variables and from a vector v of the external measured variables and external manipulated variables as follows:

{right arrow over (u)}=K·{right arrow over (y)}+L·{right arrow over (v)}, where

K is an output feedback matrix, and

L is a feedforward matrix.

The calculation of the control vector u according to the measured variables is also shown in the schematic diagram of FIG. 2. The calculation of the control vector, or in other words the control of the power generators G, the subnetworks and/or controllable loads is performed such that a dynamic behavior of the sub-grid TN with respect to its neighboring sub-grids corresponds to a defined target behavior, which in particular can be defined by an operator TSO of the interconnected grid NV. In one possible embodiment, the sub-grid controller TNR can be implemented by a central controller provided in the sub-grid TN concerned. In another possible embodiment, the sub-grid controller TNR can also be implemented in a distributed manner by means of various controllers within the sub-grid TN. The calculation of the control vector u according to the vectors y, v of the measured variables can be performed, for example, by a microprocessor executing a suitable control program.

As shown in FIG. 1, the various generators G are controlled by control variables of the control vector u. In addition, the generators G can also be affected by external disturbance variables w_(i), w_(j). For instance, the power generators or electricity generators G may be generators that produce power from renewable energies such as the wind or sun. A change in the strength of the sun and of the wind can change in an uncontrollable manner the amount of electricity produced by the generators. The disturbance vector w takes account of this change.

The sub-grid TN can comprise, in addition to the power generators G which produce power from renewable energies, also conventional power generators such as gas turbines or the like, for example.

The instantaneous state of the sub-grid TN can be calculated by the following differential equation:

{dot over ({right arrow over (x)})}=A·{right arrow over (x)}+B ₁ ·{right arrow over (u)}+B ₂ ·{right arrow over (v)}+B ₃ ·{right arrow over (w)}

where

-   {right arrow over (x)} is the state vector of the sub-grid TN, -   {right arrow over (u)} is the control vector for controlling the     controllable components within the sub-grid, -   {right arrow over (v)} is the vector of the sensor-detected external     measured variables and external manipulated variables, and -   {right arrow over (w)} is the disturbance vector.

The variables A, B₁, B₂, B₃ are matrices that define the dynamic behavior of the particular subsystem or sub-grid TN. The vector x can define the state of a sub-grid TN, for instance the charge level SOC of a battery or the states of relevant control units in a photovoltaic inverter PVI. The control vector u forms the input variable of the controllable power generators G or of the subnetworks or loads, whereas v represents external measured variables and manipulated variables, i.e. input variables which are supplied by a higher-level sub-grid TN or interconnected grid, for example by the transmission grid, for instance variables such as changes in the frequency or voltage amplitude. The disturbance vector w defines disturbances in the power generation or also load fluctuations.

The vector y of the internal measured variables of the sub-grid TN describes the internally measured variables, for instance power measurements from photovoltaic inverters PVI or smart meters, and voltage and current measurements from phasor measurement units PMUs. It can be calculated by the following equation:

{right arrow over (y)}=C·{right arrow over (x)}+D ₁ ·{right arrow over (u)}+D ₂ ·{right arrow over (v)}+D ₃ ·{right arrow over (w)}

where

-   {right arrow over (x)} is the state vector of the sub-grid, -   {right arrow over (u)} is the control vector for controlling the     controllable components within the sub-grid, -   {right arrow over (v)} is the vector of the sensor-detected external     measured variables and external manipulated variables, and -   {right arrow over (w)} is the disturbance vector     and where

C, D₁, D₂, D₃ are matrices.

In one possible embodiment, the output vector {right arrow over (z)} of the output variables of the sub-grid TN can be calculated by the following equation:

{right arrow over (z)}=E·{right arrow over (x)}+F ₁ ·{right arrow over (u)}+F ₂ ·{right arrow over (v)}+F ₃ ·{right arrow over (w)}

where

-   {right arrow over (x)} is the state vector of the sub-grid, -   {right arrow over (u)} is the control vector for controlling the     controllable components of the sub-grid, -   {right arrow over (v)} is the vector of the sensor-detected external     measured variables and external manipulated variables, and -   {right arrow over (w)} is the disturbance vector,     and where

E, F₁, F₂, F₃ are matrices.

The output-variables vector {right arrow over (z)} describes the output of the sub-grid TN to a higher-level associated sub-grid TN or to the interconnected grid, for example changes in the active-power and reactive-power feed-in to the transmission grid or neighboring sub-grids. The matrices A, B₁, B₂, B₃, C, D₁, D₂, D₃, E, F₁, F₂, F₃ used in the calculation specify the dynamic behavior of the particular subsystem or sub-grid TN. The dynamic-behavior matrix A can contain additional control requirements for the non-controllable distributed power generators, in particular for those power generators that cannot be controlled remotely but still contribute to the dynamic behavior of the sub-grid TN. These control systems can be set separately.

A defined reduced model of the sub-grid TN can be defined as follows:

{dot over (x)} _(d) =A _(d) x _(d) +B _(d) v

z _(d) =E _(d) x _(d) +F _(d) v

where

x_(d) is the state of the reduced model, and

v represents input variables from the higher-level grid. These correspond to the external measured variables and external manipulated variables of the sub-grid TN.

z_(d) represents the desired output from the sub-grid TN with respect to the higher-level sub-grid TN, where z_(d) constitutes a desired output value. The number of states of the system or of the state vector x of the dynamic system of the sub-grid TN is greater than the number of states of the reduced model x_(d).

For instance in a simple example, the sub-grid can comprise merely one connection point to an external electrical grid or transmission grid. In this simple case, the input measured-variables vector v=(f,U)^(T) depends on the voltage frequency f and the amplitude U at the connection point to the external grid.

In this simple example, the output z=(P,Q)^(T) is the active power P and the reactive power Q that is supplied to the external grid at this one connection point. In this simple example, the sub-grid TN is meant to behave as a droop controller comprising a low-pass filter. The resultant target behavior in this case is:

$x_{d}^{\prime} = {{\begin{bmatrix} {- \frac{1}{K_{p}T_{p}}} & 0 \\ 0 & {- \frac{1}{K_{Q}T_{Q}}} \end{bmatrix}x_{d}} + {\begin{bmatrix} {- \frac{1}{T_{p}}} & 0 \\ 0 & {- \frac{1}{T_{Q}}} \end{bmatrix}v}}$ $z_{d} = {\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}x_{d}}$

where z_(d)=x_(d)=(P_(d), Q_(d))^(T), i.e. is the desired active power and reactive power that is supplied to the external grid, and T_(P) and T_(Q) are the time constants of the low-pass filter for the active-power and reactive-power droop control. The power droop gains for the active power and reactive power are K_(P) and K_(Q). In the steady state, i.e. for {dot over (x)}_(d)=0, it holds that P_(d)=−K_(P)·f and Q_(d)=−K_(Q)·U, which corresponds to the conventional droop gains employed in transmission grids.

For a sub-grid having two connection points to neighboring sub-grids, the vector of the sensor-detected external measured variables is v=(f₁,U₁,f₂,U₂)^(T), and the output-variables vector is z=(P₁,Q₁,P₂,Q₂)^(T), where the indices 1, 2 for the measured variables f, U, P, Q indicate the connection point with which the relevant value is associated. A reduced model, similar to the model presented above, in this case is given by:

${\overset{.}{x}}_{d} = \begin{matrix} {{\begin{bmatrix} {- \frac{1}{K_{P\; 1}T_{P\; 1}}} & 0 & 0 & 0 \\ 0 & {- \frac{1}{K_{Q\; 1}T_{Q\; 1}}} & 0 & 0 \\ 0 & 0 & {- \frac{1}{K_{P\; 2}T_{P\; 2}}} & 0 \\ 0 & 0 & 0 & {- \frac{1}{K_{Q\; 2}T_{Q\; 2}}} \end{bmatrix}x_{d}} +} \\ \begin{bmatrix} {- \frac{1}{T_{P\; 1}}} & 0 & 0 & 0 \\ 0 & {- \frac{1}{T_{Q\; 1}}} & 0 & 0 \\ 0 & 0 & {- \frac{1}{T_{P\; 2}}} & 0 \\ 0 & 0 & 0 & {- \frac{1}{T_{Q\; 2}}} \end{bmatrix} \end{matrix}$ $z_{d} = {\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}x_{d}}$

where each connection point or connection line VL has its own active-power and reactive-power droop gain K_(Pi), K_(Qi), i=1, 2, and active-power and reactive-power time constants T_(Pi), T_(Qi) i=1, 2.

The sub-grid controller TNR according to the invention may constitute a static or dynamic controller for which the control vector for the power generators G is calculated from the vector y of the internal measured variables and a vector v of the external measured variables and manipulated variables as follows: u=K·y+L·v,

where the control vector u is calculated so as to make the error z−z_(d) practically zero, and said control vector u for the controlled power generators, loads and subnetworks depends on the measured variables y within the sub-grid and on the external measured variables v of the sub-grid. It is possible here to take into account the special situation in which the vector v of the external measured variables is not measured, i.e. in which the feedforward matrix L equals 0 (L=0). The term z−z_(d) being practically zero can be expressed using various signal-norm and system-norm notations such as H₂ or H_(∞).

In one possible embodiment, the sub-grid controller TNR can be designed or implemented by a design algorithm for the control matrices K and L on the basis of a H_(∞) system norm. In this case, the external input variables v and w are considered to be deterministically arbitrary but power-limited signals. A value γ can be defined as the upper limit of a ratio between the l₂ norm of the controller error e=z−z_(d) and the l₂ norm of (v,w)^(T), i.e.:

$\gamma \geq {\max\limits_{{{({v,w})}^{T}}_{2} \neq 0}{\frac{{e}_{2}}{{\begin{pmatrix} v \\ v \end{pmatrix}}_{2}}.}}$

The smaller this value γ is, the smaller the effect of the measured variables v and the disturbance variables w on the error e and hence on the difference between the output value z and setpoint value z_(d). The resultant sub-grid controller TNR can be designed such that the effect of both v and w on z−z_(d) can be minimized. It can be assumed by way of example for illustrative purposes that the matrices D₁, D₂, D₃, F₁, F₂, F₃, F_(d) equal zero. Similar results can be obtained when these matrices are non-zero. The following is obtained:

{dot over (x)}=(A+B ₁ KC)x+(B ₂ +B ₁ L)v+B ₃ w

z=Ex

where for designing the output feedback matrix K and the feedforward matrix L a new system can be formulated as follows:

$\begin{bmatrix} \overset{.}{x} \\ {\overset{.}{x}}_{d} \\ e \end{bmatrix} = {\begin{bmatrix} {A + {B_{1}{KC}}} & 0 & {B_{2} + {B_{1}L}} & B_{3} \\ 0 & A_{d} & B_{d} & 0 \\ E & {- E_{d}} & 0 & 0 \end{bmatrix}\begin{bmatrix} x \\ x_{d} \\ v \\ w \end{bmatrix}}$

Hence the output feedback matrix K and the feedforward matrix L must be designed to minimize γ, i.e. the error e lies as close as possible to zero for power-limited w and v. One possible solution lies in the following optimization problem:

$\mspace{20mu} {\min\limits_{P,K,L}\mspace{14mu} \gamma}$ $\mspace{20mu} {{s.t.\mspace{14mu} P} = {P^{T} \succ {0\begin{bmatrix} {{\begin{bmatrix} \begin{matrix} {A +} \\ {B_{1}{KC}} \end{matrix} & 0 \\ 0 & A_{d} \end{bmatrix}^{T}P} + {P\begin{bmatrix} \begin{matrix} {A +} \\ {B_{1}{KC}} \end{matrix} & 0 \\ 0 & A_{d} \end{bmatrix}}} & {P\begin{bmatrix} {B_{2} + {B_{1}L}} & B_{3} \\ B_{d} & 0 \end{bmatrix}} & \begin{bmatrix} E \\ {- E_{d}} \end{bmatrix} \\ {\begin{bmatrix} \begin{matrix} {B_{2} +} \\ {B_{1}L} \end{matrix} & B_{3} \\ B_{d} & 0 \end{bmatrix}^{T}P} & {{- \gamma}\; I} & 0 \\ \left( {E - E_{d}} \right) & 0 & {{- \gamma}\; I} \end{bmatrix}} \prec 0}}$

where P is a square matrix of optimization variables of the dimension of A plus the dimension of A_(d), and where I is the identity matrix and >0, <0 represents the positive or negative definiteness of the corresponding matrices.

The optimization problem presented above is not convex because the bilinear matrix inequality BMI contains products of the matrix P and the output feedback matrix K and the feedforward matrix L. Standard algorithms for BMIs can be used in order to solve this optimization problem. Similar algorithms can be derived for the following cases:

(1) The controller cannot measure or detect the external measured variables and hence the feedforward matrix equals 0 (L=0).

(2) Locally implemented sub-grid controllers TNR can be configured, which use only local measured variables, where the output feedback matrix K, with suitable sorting of the vectors y and u, is a diagonal matrix, and the feedforward matrix L is zero (L=0).

(3) A dynamic sub-grid controller TNR of the following form can be used:

{dot over (x)}=A _(c) x _(c) +B _(c1) y+B _(c2) v

u=C _(c) x _(c) +D _(c1) y+D _(c2) v

where all the matrices A_(c), B_(c1), B_(c2), C_(c), D_(c1), D_(c2) are formulated or implemented in a suitable algorithm.

The sub-grid controller TNR according to the invention or the method according to the invention for controlling components of a sub-grid TN within an interconnected grid NV is suitable in particular for sub-grids that contain a high proportion of power generators that produce power from renewable energy sources. The relevant sub-grid operators DSO can use suitable design algorithms to design the sub-grid controller TNR and the dynamic behavior. In addition, a suitable design algorithm can be used by the interconnected-grid operator TSO for a country-wide design of the interconnected grid. The sub-grid controller TNR controls power generators or loads of the sub-grid TN according to measured variables of the sub-grid TN in such a way that the dynamic behavior of the sub-grid TN concerned, as operated by the relevant sub-grid operator DSO, with respect to its neighboring sub-grids corresponds to a defined target behavior, which can be defined, for example, by an operator TSO of the interconnected grid. The sub-grid controller TNR is thus designed in accordance with the target behavior that is defined by the interconnected-grid operator TSO. The dynamic behavior of the sub-grid TN can be configured accordingly. 

1. A sub-grid controller for a sub-grid within an interconnected grid, the sub-grid controller comprising: a first controller configured to control power generators, subnetworks, or loads of the sub-grid according to sensor-detected internal measured variables, sensor-detected external measured variables and external manipulated variables, or a combination thereof of the sub-grid, such that a dynamic behavior of the sub-grid with respect to neighboring sub-grids corresponds to a defined target behavior.
 2. The sub-grid controller of claim 1, wherein the first controller receives from an operator of the interconnected grid a target behavior for stabilizing the interconnected gird.
 3. The sub-grid controller of claim 1, wherein the first controller is configured to calculate a control vector for the power generators, loads, and subnetworks from a vector of the internal measured variables and a vector of the external measured variables and external manipulated variables as follows: {right arrow over (u)}=K·{right arrow over (y)}+L·{right arrow over (v)}, where K is an output feedback matrix, and L is a feedforward matrix.
 4. The sub-grid controller of claim 1, wherein the external measured variables of the sub-grid are detected by sensors, that are arranged on connecting lines between the sub-grid and neighboring sub-grids.
 5. The sub-grid controller of claim 1, wherein the internal measured variables are detected by sensors that are arranged on lines or devices within the sub-grid.
 6. The sub-grid controller of claim 1, wherein an instantaneous state of the sub-grid is calculable by the following differential equation: {dot over (x)}=A·{right arrow over (x)}+B ₁ ·{right arrow over (u)}+B ₂ ·{right arrow over (v)}+B ₃ ·{right arrow over (w)} wherein {right arrow over (x)} is the state vector of the sub-grid, u is the control vector for controlling the controllable power generators, loads and subnetworks within the sub-grid, {right arrow over (v)} is the vector of the sensor-detected external measured variables and external manipulated variables, and {right arrow over (w)} is the disturbance vector, and wherein A, B₁, B₂, B₃ are matrices.
 7. The sub-grid controller of claim 3, wherein the vector of the internal measured variables of the sub-grid is calculable by the following equation: {right arrow over (y)}=C·{right arrow over (x)}+D ₁ ·u+D ₂ ·{right arrow over (v)}+D ₃ ·{right arrow over (w)} wherein {right arrow over (x)} is the state vector of the sub-grid, {right arrow over (u)} is the control vector for controlling the controllable power generators, loads and subnetworks within the sub-grid, {right arrow over (v)} is the vector of the sensor-detected external measured variables and external manipulated variables, and {right arrow over (w)} is the disturbance vector, and wherein C, D₁, D₂, D₃ are matrices.
 8. The sub-grid controller of claim 1, wherein an output vector of the output variables of the sub-grid is calculable by the following equation: {right arrow over (z)}=E·{right arrow over (x)}+F ₁ ·{right arrow over (u)}+F ₂ ·{right arrow over (v)}+F ₃ ·{right arrow over (w)} wherein {right arrow over (x)} is the state vector of the sub-grid, {right arrow over (u)} is the control vector for controlling the controllable power generators, loads and subnetworks within the sub-grid, {right arrow over (v)} is the vector of the sensor-detected external measured variables and the external manipulated variables, and W is the disturbance vector, and wherein E, F₁, F₂, F₃ are matrices.
 9. The sub-grid controller of claim 1, wherein the first controller is a central controller provided in the sub-grid concerned or a controller that is implemented in the sub-grid in a distributed manner.
 10. The sub-grid controller of claim 1, wherein the sub-grid controller controls power generators, loads, and/or subnetworks, or any combination thereof within a power distribution grid or configures the local controllers of the power generators, loads, subnetworks, or any combination thereof.
 11. An interconnected grid comprising: a plurality of sub-grids, each sub-grid of the plurality of sub-grids comprising a sub-grid controller configured to control power generators, subnetworks, or loads of the sub-grid according to sensor-detected internal measured variables, sensor-detected external measured variables and external manipulated variables, or a combination thereof of the sub-grid, such that a dynamic behavior of the sub-grid with respect to neighboring sub-grids corresponds to a defined target behavior.
 12. The interconnected grid of claim 11, wherein each sub-grid of the plurality of sub-grids comprises controllable, configurable, or controllable and configurable power generators, subnetworks, loads, or any combination thereof.
 13. A method for controlling units of a sub-grid within an interconnected grid, the method comprising: detecting, using sensors, internal and external measured variables of the sub-grid; controlling power generators, subnetworks, or loads of the sub-grid according to the sensor-detected measured variables and external manipulated variables such that a dynamic behavior of the sub-grid with respect to neighboring sub-grids corresponds to a defined target behavior.
 14. The method of claim 13, wherein the target behavior of the sub-grid is defined or set by an operator of the interconnected grid.
 15. A sub-grid controller comprising: a microprocessor configured to control power generators, subnetworks, or loads of the sub-grid according to sensor-detected internal measured variables, sensor-detected external measured variables and external manipulated variables, or a combination thereof of the sub-grid, such that a dynamic behavior of the sub-grid with respect to neighboring sub-grids corresponds to a defined target behavior. 